Model and solve -3 1/2 + 2 3/4 on the vertical number line. Start at the first value and show the signed movement.
The filled point is the starting value. Draw the signed movement and endpoint; reveal answers only when checking work.
CCSS 7.NS.A.1b–c · horizontal & vertical number lines
Add and Subtract Rational Numbers on Number Lines
Model signed addition and subtraction as movement rather than memorized sign rules. Problems use exact integer, half, third, or quarter tick positions and rotate between horizontal and vertical number lines.
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Rational Numbers on Number Lines
Number-line addition & subtraction · Grade 7 standard · Seed 271701
1.
2.
Model and solve -1 1/2 - 2 on the horizontal number line. Start at the first value and show the signed movement.
The filled point is the starting value. Draw the signed movement and endpoint; reveal answers only when checking work.
3.
Model and solve 1/4 - (-3) on the horizontal number line. Start at the first value and show the signed movement.
The filled point is the starting value. Draw the signed movement and endpoint; reveal answers only when checking work.
4.
Model and solve -2 1/4 + 3 on the vertical number line. Start at the first value and show the signed movement.
The filled point is the starting value. Draw the signed movement and endpoint; reveal answers only when checking work.
5.
Model and solve 1/2 - (-1) on the vertical number line. Start at the first value and show the signed movement.
The filled point is the starting value. Draw the signed movement and endpoint; reveal answers only when checking work.
6.
Model and solve -1/2 + (-1/4) on the vertical number line. Start at the first value and show the signed movement.
The filled point is the starting value. Draw the signed movement and endpoint; reveal answers only when checking work.
7.
Model and solve 3 1/2 - 1 on the horizontal number line. Start at the first value and show the signed movement.
The filled point is the starting value. Draw the signed movement and endpoint; reveal answers only when checking work.
8.
Model and solve 4 + (-1) on the horizontal number line. Start at the first value and show the signed movement.
The filled point is the starting value. Draw the signed movement and endpoint; reveal answers only when checking work.
9.
Model and solve -1 - (-1 1/2) on the horizontal number line. Start at the first value and show the signed movement.
The filled point is the starting value. Draw the signed movement and endpoint; reveal answers only when checking work.
10.
Model and solve 3 - 1 on the vertical number line. Start at the first value and show the signed movement.
The filled point is the starting value. Draw the signed movement and endpoint; reveal answers only when checking work.
Exact-construction rule: operations use normalized integer numerator/denominator pairs, number-line positions use exact ticks, repeating decimals come from remainder cycles, and money contexts use exact cents. No answer depends on binary floating-point rounding.
Teaching note 1
For p + q, start at p and move in the direction indicated by the sign of q.
Teaching note 2
For p - q, rewrite as p + (-q) before deciding the direction of movement.
Teaching note 3
The distance between two rational numbers is the absolute value of their difference, regardless of left/right or up/down order.
Continue the 7.NS progression
Move to another Grade 7 rational-number skill
Frequently asked questions
Do the lines include fractions?
Yes. Depending on level, the line can use whole-number, half, third, or quarter-unit ticks.
Why include vertical number lines?
The Grade 7 standard explicitly allows horizontal or vertical number-line diagrams, and vertical lines connect naturally to temperature and elevation contexts.